Varieties of Distributivity: One by One vs Each

Consider the contrast in interpretation between the examples in (1) and (2) below. While example (1) is compatible with events that unfold in very different ways, the addition of one by one in (2) constrains how the leaving events can proceed. Intuitively, one by one is an event modifier that targets a plural participant in the event. More precisely, it breaks the event down into temporally sequenced subevents and it distributes the plural participant over these subevents, as depicted in (3) below.